Details

analyze767.0ms (20.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
25%	75%	0%	4
37.5%	62.5%	0%	5
43.7%	56.2%	0%	6
46.9%	53.1%	0%	7
46.9%	53.1%	0%	8
46.9%	53.1%	0%	9
47.2%	52.7%	0%	10
47.2%	52.7%	0%	11
47.3%	52.7%	0%	12
47.3%	52.7%	0%	13
47.3%	52.6%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (52.1%)

Results

985.0ms	2178×	body	2048	valid
432.0ms	4233×	body	128	valid
354.0ms	1047×	body	1024	valid
134.0ms	531×	body	512	valid
46.0ms	267×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

15.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	0.8b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series4.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

2.0ms	(atan.f64 (+.f64 N 1))
2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
392×	`unsub-neg_binary64`
319×	`distribute-rgt-in_binary64`
308×	`unswap-sqr_binary64`
275×	`times-frac_binary64`

Counts

40 → 48

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	72	836
1	128	555
2	354	501
3	1262	498
4	2924	498
5	4651	491
6	4824	491

prune39.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	2	49

Error

0.4b

Counts

49 → 2

Alt Table

Status	Error	Program
	15.2b	(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (fma.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (*.f64 (atan.f64 N) (atan.f64 N))))
▶	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Status

Error

Program

15.2b

(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (fma.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (*.f64 (atan.f64 N) (atan.f64 N))))

▶

0.4b

(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 968 to 539 computations (44.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (fma.f64 N N N))
✓	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series4.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

2.0ms	(+.f64 1 (fma.f64 N N N))
2.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 1 (fma.f64 N N N))
0.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

832×	`sub-neg_binary64`
634×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
319×	`associate-l_binary64`
301×	`associate-r_binary64`

Counts

39 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	435
1	98	377
2	243	377
3	899	377
4	2950	377
5	4669	377
6	5438	377

prune50.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	47	6	53
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	49	6	55

Error

0.4b

Counts

55 → 6

Alt Table

Status	Error	Program
	0.9b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	1.6b	(.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	10.0b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))
	1.8b	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
▶	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
	10.2b	(atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3)))

Compiler

Compiled 870 to 538 computations (38.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 N (fma.f64 N N 1))
✓	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

series4.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

2.0ms	(+.f64 N (fma.f64 N N 1))
2.0ms	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 N (fma.f64 N N 1))
0.0ms	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

simplify79.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

360×	`associate--r+_binary64`
356×	`associate-l_binary64`
276×	`associate-+l-_binary64`
256×	`associate-r_binary64`
239×	`associate--l+_binary64`

Counts

39 → 41

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	45	435
1	103	389
2	264	386
3	994	386
4	2167	381
5	4689	381
6	4925	381
7	4923	381

prune35.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	41	6	47

Error

0.4b

Counts

47 → 6

Alt Table

Status	Error	Program
▶	0.9b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	1.6b	(.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	10.0b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))
	1.8b	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	25.9b	(atan2.f64 1 (/.f64 (-.f64 -1 (*.f64 N (+.f64 N (pow.f64 N 3)))) (-.f64 N (fma.f64 N N 1))))
✓	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

Compiler

Compiled 707 to 467 computations (33.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (fma.f64 N N N))
	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.6b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	16.7b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series6.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify116.0ms (3%)

Algorithm

1×	egg-herbie

Rules

498×	`log-prod_binary64`
465×	`*-commutative_binary64`
441×	`unswap-sqr_binary64`
425×	`log-div_binary64`
306×	`sqr-pow_binary64`

Counts

80 → 75

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	52	1385
1	75	1281
2	181	1233
3	389	1149
4	720	1054
5	1324	1054
6	2519	1040
7	4285	1040
8	4994	1040
9	4835	1040

prune190.0ms (5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	196	7	203

Error

0.4b

Counts

203 → 7

Alt Table

Status	Error	Program
	1.8b	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	25.9b	(atan2.f64 1 (/.f64 (-.f64 -1 (*.f64 N (+.f64 N (pow.f64 N 3)))) (-.f64 N (fma.f64 N N 1))))
	6.8b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))
	10.0b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))
	1.6b	(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

Compiler

Compiled 4903 to 3041 computations (38% saved)

regimes210.0ms (5.5%)

Accuracy

Total 0.0b remaining (10.4%)

Threshold costs 0.0b (10.4%)

Counts

108 → 1

Compiler

Compiled 4329 to 2921 computations (32.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	9	11
2	8	11

end111.0ms (2.9%)

Compiler: Compiled 146 to 100 computations (31.5% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze767.0ms (20.2%)

sample2.0s (52.1%)

simplify10.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify71.0ms (1.9%)

prune39.0ms (1%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify71.0ms (1.9%)

prune50.0ms (1.3%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify79.0ms (2.1%)

prune35.0ms (0.9%)

localize12.0ms (0.3%)

series6.0ms (0.2%)

rewrite11.0ms (0.3%)

simplify116.0ms (3%)

prune190.0ms (5%)

regimes210.0ms (5.5%)

simplify2.0ms (0.1%)

end111.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11